On degeneracy and invariances of random fields paths with applications in Gaussian process modelling

We study pathwise invariances and degeneracies of random fields with motivating applications in Gaussian process modelling. The key idea is that a number of structural properties one may wish to impose a priori on functions boil down to degeneracy properties under well-chosen linear operators. We first show in a second order set-up that almost sure degeneracy of random field paths under some class of linear operators defined in terms of signed measures can be controlled through the two first moments. A special focus is then put on the Gaussian case, where these results are revisited and extended to further linear operators thanks to state-of-the-art representations. Several degeneracy properties are tackled, including random fields with symmetric paths, centred paths, harmonic paths, or sparse paths. The proposed approach delivers a number of promising results and perspectives in Gaussian process modelling. In a first numerical experiment, it is shown that dedicated kernels can be used to infer an axis of symmetry. Our second numerical experiment deals with conditional simulations of a solution to the heat equation, and it is found that adapted kernels notably enable improved predictions of non-linear functionals of the field such as its maximum.

The nociceptive withdrawal reflex: Normative values of thresholds and reflex receptive fields

Assessments of spinal nociceptive withdrawal reflexes can be used in human research both to evaluate the effect of analgesics and explore pain mechanisms related to sensitization. Before the reflex can be used as a clinical tool, normative values need to be determined in large scale studies. The aim of this study was to determine the reference values of spinal nociceptive reflexes and subjective pain thresholds (to single and repeated stimulation), and of the area of the reflex receptive fields (RRF) in 300 pain-free volunteers. The influences of gender, age, height, weight, body-mass index (BMI), body side of testing, depression, anxiety, catastrophizing and parameters of Short-Form 36 (SF-36) were analyzed by multiple regressions. The 95% confidence intervals were determined for all the tests as normative values. Age had a statistically and quantitatively significant impact on the subjective pain threshold to single stimuli. The reflex threshold to single stimulus was lower on the dominant compared to the non-dominant side. Depression had a negative impact on the subjective pain threshold to single stimuli. All the other analyses either did not reveal statistical significance or displayed quantitatively insignificant correlations. In conclusion, normative values of parameters related to the spinal nociceptive reflex were determined. This allows their clinical application for assessing central hyperexcitability in individual patients. The parameters investigated explore different aspects of sensitization processes that are largely independent of demographic characteristics, cognitive and affective factors.

Generalized expansion of nociceptive reflex receptive fields in chronic pain patients

Widespread central hypersensitivity is present in chronic pain and contributes to pain and disability. According to animal studies, expansion of receptive fields of spinal cord neurons is involved in central hypersensitivity. We recently developed a method to quantify nociceptive receptive fields in humans using spinal withdrawal reflexes. Here we hypothesized that patients with chronic pelvic pain display enlarged reflex receptive fields. Secondary endpoints were subjective pain thresholds and nociceptive withdrawal reflex thresholds after single and repeated (temporal summation) electrical stimulation. 20 patients and 25 pain-free subjects were tested. Electrical stimuli were applied to 10 sites on the foot sole for evoking reflexes in the tibialis anterior muscle. The reflex receptive field was defined as the area of the foot (fraction of the foot sole) from which a muscle contraction was evoked. For the secondary endpoints, the stimuli were applied to the cutaneous innervation area of the sural nerve. Medians (25-75 percentiles) of fraction of the foot sole in patients and controls were 0.48 (0.38-0.54) and 0.33 (0.27-0.39), respectively (P=0.008). Pain and reflex thresholds after sural nerve stimulation were significantly lower in patients than in controls (P<0.001 for all measurements). This study provides for the first time evidence for widespread expansion of reflex receptive fields in chronic pain patients. It thereby identifies a mechanism involved in central hypersensitivity in human chronic pain. Reverting the expansion of nociceptive receptive fields and exploring the prognostic meaning of this phenomenon may become future targets of clinical research.

Spontaneous recovery of visually-triggered saccades after focal lesions of the frontal and parietal eye fields: A combined longitudinal oculomotor and fMRI study

To analyze oculomotor recovery in a patient with ischemic lesions restricted to the left frontal eye field (FEF) and the left parietal eye field (PEF).

The importance of ship log data: reconstructing North Atlantic, European and Mediterranean sea level pressure fields back to 1750

Local to regional climate anomalies are to a large extent determined by the state of the atmospheric circulation. The knowledge of large-scale sea level pressure (SLP) variations in former times is therefore crucial when addressing past climate changes across Europe and the Mediterranean. However, currently available SLP reconstructions lack data from the ocean, particularly in the pre-1850 period. Here we present a new statistically-derived 5�� �� 5�� resolved gridded seasonal SLP dataset covering the eastern North Atlantic, Europe and the Mediterranean area (40��W���50��E; 20��N���70��N) back to 1750 using terrestrial instrumental pressure series and marine wind information from ship logbooks. For the period 1750���1850, the new SLP reconstruction provides a more accurate representation of the strength of the winter westerlies as well as the location and variability of the Azores High than currently available multiproxy pressure field reconstructions. These findings strongly support the potential of ship logbooks as an important source to determine past circulation variations especially for the pre-1850 period. This new dataset can be further used for dynamical studies relating large-scale atmospheric circulation to temperature and precipitation variability over the Mediterranean and Eurasia, for the comparison with outputs from GCMs as well as for detection and attribution studies.